# We've inserted comment lines, which begin with a '#',

*Command lines* begin with a '>'. You should enter everything after the '>' and hit return. R's response will be in the line or lines below the command.

**Trick**: you can use the up arrow to find previous commands.

`>`

. It's probably the
window in the lower left.
```
> 2+3
[1] 5
> 2*3
[1] 6
> 2/3
[1] 0.6666667
> 2^3
[1] 8
> 2*(3+1)^2
[1] 32
```

Don't worry for now about the `[1]`

. It is there for when R is printing numbers in a list.
```
> x = 2+3
# When you assign a value to a variable it does not echo the answer to the screen. You can see the value of
````x`

by just using `x`

as a command.
>x
[1] 5
> y = 1+2
> x*y
[1] 15
> z = x^y
> z
[1] 125
# R has another notation for assignment: the arrow: `<-`

. Many R programmers use this. It may seem odd to programmers coming from other languages.
> x <- 3
> x
[1] 3
> x <- 5.412
> x
[1] 5.412

# You create vectors by using the

`c()`

function.
```
# A vector with 4 entries
> c(1, 2, 3, 4)
[1] 1 2 3 4
# You can store vectors in variables.
> x = c(1.1, 0.0, 3.14, 2.718)
> x
[1] 1.100 0.000 3.140 2.718
# Of course using the arrow instead of equal sign works here.
> x <- c(2,4,6)
> x
[1] 2 4 6
# Sequences of integers are so common there is a shortcut for making them.
> 1:4
[1] 1 2 3 4
> 3:10
[1] 3 4 5 6 7 8 9 10
> 9:2
[1] 9 8 7 6 5 4 3 2
# A long vector will be displayed over several lines. At
the start of each line in brackets is the index of the first entry on that line.
> x = 1:40
> x
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
[24] 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
```

```
```

```
> x = c(1,3,5)
> x + 7.1
[1] 8.1 10.1 12.1
# Subtraction, multiplication, division and powers work the same way.
> x = c(1,3,5)
> 7*x
[1] 7 21 35
> x/7
[1] 0.1428571 0.4285714 0.7142857
> 7/x
[1] 7.000000 2.333333 1.400000
> x^6
[1] 1 729 15625
> x^7
[1] 1 2187 78125
> 7^x
[1] 7 343 16807
```

# You can add, subtract, multiply and divide vectors of # Check that the following give the right answers.

```
> x = c(1,2,3)
≫ y = c(4,5,6)
> x+y
[1] 5 7 9
> x-y
[1] -3 -3 -3
> z = x*y
> z
[1] 4 10 18
> z = x/y
> z
[1] 0.25 0.40 0.50
# You can even raise a vector to another vector of the same length
> x^y
[1] 1 32 729
```

```
# Entries in vectors are found with the notation x[j]
> x = c(2,4,6,8,10)
> x[1]
[1] 2
> x[2]
[1] 4
> x[3]
[1] 6
> x[4]
[1] 8
# R allows you to access more than one entry at a time
# x has 8 elements
> x = 2*c(1,2,3,4,5,6,7,8)
> x
[1] 2 4 6 8 10 12 14 16
# Notice that we have to put a vector of indices inside the brackets to access the first and second entries in x
> x[c(1,2)]
[1] 2 4
> x[c(1,3,5)]
[1] 2 6 10
# We can access the same entry multiple times.
> x[c(2,2,2,1)]
[1] 4 4 4 2
# Using the colon method of creating vectors is useful here.
> x[2:5]
[1] 4 6 8 10
```

```
# We'll start with functions numbers
> sin(1)
[1] 0.841471
> sin(1.4)
[1] 0.9854497
> sin(3)
[1] 0.14112
# R knows about pi
> pi
[1] 3.141593
> sin(pi/2)
[1] 1
> sin(pi/2)
# The exponential function is given by 'exp'.
> exp(0)
[1] 1
> exp(1)
[1] 2.718282
# Sin acts on vectorsby taking the sin of each element.
> x = c(1,2,3,4)
> x
[1] 1 2 3 4
> sin(x)
[1] 0.8414710 0.9092974 0.1411200 -0.7568025
# exp also acts on vectors.
> x = c(1,2,3,4)
> exp(x)
[1] 2.718282 7.389056 20.085537 54.598150
# In 18.05 we will use the sum and mean functions on vectors. They take the sum and average respectively of the vectors entries
> x = 1:6
> x
[1] 1 2 3 4 5 6
> sum(x)
[1] 21
> mean(x)
[1] 3.5
# Example: find the sum of the integers from 1 to 1024.
> x = 1:1024
> sum(x)
[1] 524800
# This can be done in one command.
> sum(1:1024)
[1] 524800
```

```
# Example: find the sum of the squares of the integers from 1 to 1024.
> x = 1:1024
> sum(x^2)
[1] 358438400
# This can be done in one command.
> sum((1:1024)^2)
[1] 358438400
```

```
# A vector of length 10 can be arranged as
a 2x5 or a 5x2 matrix
# Again the syntax is clunky but very clear
> x = 1:10
> x
[1] 1 2 3 4 5 6 7 8 9 10
> y = matrix(x,nrow=2,ncol=5)
> y
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 5 7 9
[2,] 2 4 6 8 10
> z = matrix(x,nrow=5,ncol=2)
> z
[,1] [,2]
[1,] 1 6
[2,] 2 7
[3,] 3 8
[4,] 4 9
[5,] 5 10
# Notice in the examples above R build the matrices one column at a time. That is our vector 1 to 10 runs in sequence down the columns. For 18.05 this is usually fine.
# However the matrix() function, like most R function, has a lot of optional parameters that allow you to control its behavior. Here's how to make it buid a matrix by rows
> z = matrix(x,nrow=2,ncol=5, byrow = TRUE)
> z
[,1] [,2] [,3] [,4] [,5]
[1,] 1 2 3 4 5
[2,] 6 7 8 9 10
```

```
> x = 1:10
> y = matrix(x,nrow=2,ncol=5)
> y
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 5 7 9
[2,] 2 4 6 8 10
> y[1,1]
[1] 1
> y[2,3]
[1] 6
```

```
# Start by creating a matrix to practice on.
> x = 1:10
> y = matrix(x,nrow=2,ncol=5)
> y
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 5 7 9
[2,] 2 4 6 8 10
# To sum each of the columns we use the colSums function.
> y
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 5 7 9
[2,] 2 4 6 8 10
# y has two rows so rowSums(y) produces 2 numbers.
> rowSums(y)
[1] 25 30
# y has five co so colSums(y) produces 5 numbers.
> colSums(y)
[1] 3 7 11 15 19
# Likewise rowMeans(y) and colMeans(y):
> rowMeans(y)
[1] 5 6
> colMeans(y)
[1] 1.5 3.5 5.5 7.5 9.5
```

```
# R and RStudio have complete documentation on all R functions. The lower right window in RStudio has a help tab you can use. The help contains a lot of information, so you will have to learn to filter out what you don't need.
# Usually faster is to ask for help from the command line using a question mark.
> ?mean
# Try it, the result will appear in the help window.
```